package com.yc.matric;

/******************************************************************************
 * Compilation:  javac Complex.java
 * Execution:    java Complex
 * <p/>
 * Data type for complex numbers.
 * <p/>
 * The data type is "immutable" so once you create and initialize
 * a Complex object, you cannot change it. The "final" keyword
 * when declaring re and im enforces this rule, making it a
 * compile-time error to change the .re or .im fields after
 * they've been initialized.
 * <p/>
 * % java Complex
 * a            = 5.0 + 6.0i
 * b            = -3.0 + 4.0i
 * Re(a)        = 5.0
 * Im(a)        = 6.0
 * b + a        = 2.0 + 10.0i
 * a - b        = 8.0 + 2.0i
 * a * b        = -39.0 + 2.0i
 * b * a        = -39.0 + 2.0i
 * a / b        = 0.36 - 1.52i
 * (a / b) * b  = 5.0 + 6.0i
 * conj(a)      = 5.0 - 6.0i
 * |a|          = 7.810249675906654
 * tan(a)       = -6.685231390246571E-6 + 1.0000103108981198i
 ******************************************************************************/

public class Complex {
    private final double re;   // the real part
    private final double im;   // the imaginary part

    // create a new object with the given real and imaginary parts
    public Complex(double real, double imag) {
        re = real;
        im = imag;
    }

    // return a string representation of the invoking Complex object
    public String toString() {
        if (im == 0) return re + "";
        if (re == 0) return im + "i";
        if (im < 0) return re + " - " + (-im) + "i";
        return re + " + " + im + "i";
    }

    // return abs/modulus/magnitude and angle/phase/argument
    public double abs() {
        return Math.hypot(re, im);
    }  // Math.sqrt(re*re + im*im)

    public double phase() {
        return Math.atan2(im, re);
    }  // between -pi and pi

    // return a new Complex object whose value is (this + b)
    public Complex plus(Complex b) {
        Complex a = this;             // invoking object
        double real = a.re + b.re;
        double imag = a.im + b.im;
        return new Complex(real, imag);
    }

    // return a new Complex object whose value is (this - b)
    public Complex minus(Complex b) {
        Complex a = this;
        double real = a.re - b.re;
        double imag = a.im - b.im;
        return new Complex(real, imag);
    }

    // return a new Complex object whose value is (this * b)
    public Complex times(Complex b) {
        Complex a = this;
        double real = a.re * b.re - a.im * b.im;
        double imag = a.re * b.im + a.im * b.re;
        return new Complex(real, imag);
    }

    // scalar multiplication
    // return a new object whose value is (this * alpha)
    public Complex times(double alpha) {
        return new Complex(alpha * re, alpha * im);
    }

    // return a new Complex object whose value is the conjugate of this
    public Complex conjugate() {
        return new Complex(re, -im);
    }

    // return a new Complex object whose value is the reciprocal of this
    public Complex reciprocal() {
        double scale = re * re + im * im;
        return new Complex(re / scale, -im / scale);
    }

    // return the real or imaginary part
    public double re() {
        return re;
    }

    public double im() {
        return im;
    }

    // return a / b
    public Complex divides(Complex b) {
        Complex a = this;
        return a.times(b.reciprocal());
    }

    // return a new Complex object whose value is the complex exponential of this
    public Complex exp() {
        return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));
    }

    // return a new Complex object whose value is the complex sine of this
    public Complex sin() {
        return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));
    }

    // return a new Complex object whose value is the complex cosine of this
    public Complex cos() {
        return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
    }

    // return a new Complex object whose value is the complex tangent of this
    public Complex tan() {
        return sin().divides(cos());
    }


    // a static version of plus
    public static Complex plus(Complex a, Complex b) {
        double real = a.re + b.re;
        double imag = a.im + b.im;
        Complex sum = new Complex(real, imag);
        return sum;
    }

//    public static void main(String[] args) {
//        Complex a = new Complex(5.0, 6.0);
//        Complex b = new Complex(-3.0, 4.0);
//
//        System.out.println("a            = " + a);
//        System.out.println("b            = " + b);
//        System.out.println("Re(a)        = " + a.re());
//        System.out.println("Im(a)        = " + a.im());
//        System.out.println("b + a        = " + b.plus(a));
//        System.out.println("a - b        = " + a.minus(b));
//        System.out.println("a * b        = " + a.times(b));
//        System.out.println("b * a        = " + b.times(a));
//        System.out.println("a / b        = " + a.divides(b));
//        System.out.println("(a / b) * b  = " + a.divides(b).times(b));
//        System.out.println("conj(a)      = " + a.conjugate());
//        System.out.println("|a|          = " + a.abs());
//        System.out.println("tan(a)       = " + a.tan());
//    }

}
